Bias versus variance when fitting multi-species molecular lines with a non-LTE radiative transfer model: Application to the estimation of the gas temperature and volume density
Artikel i vetenskaplig tidskrift, 2024
Context. Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines. Aims. We study several hypotheses that enable robust estimations of the column densities and physical conditions when fitting one or two transitions per molecular species. We study the extent to which simplifying assumptions aimed at reducing the complexity of the problem introduce estimation biases and how to detect them. Methods. We focus on the CO and HCO+ isotopologues and analyze maps of a 50 square arcminutes field. We used the RADEX escape probability model to solve the statistical equilibrium equations and compute the emerging line profiles, assuming that all species coexist. Depending on the considered set of species, we also fixed the abundance ratio between some species and explored different values. We proposed a maximum likelihood estimator to infer the physical conditions and considered the effect of both the thermal noise and calibration uncertainty. We analyzed any potential biases induced by model misspecifications by comparing the results on the actual data for several sets of species and confirmed with Monte Carlo simulations. The variance of the estimations and the efficiency of the estimator were studied based on the Cramér-Rao lower bound. Results. Column densities can be estimated with 30% accuracy, while the best estimations of the volume density are found to be within a factor of two. Under the chosen model framework, the peak 12CO (1 -0) is useful for constraining the kinetic temperature. The thermal pressure is better and more robustly estimated than the volume density and kinetic temperature separately. Analyzing CO and HCO+ isotopologues and fitting the full line profile are recommended practices with respect to detecting possible biases. Conclusions. Combining a non-local thermodynamic equilibrium model with a rigorous analysis of the accuracy allows us to obtain an efficient estimator and identify where the model is misspecified. We note that other combinations of molecular lines could be studied in the future.
ISM: general
Methods: data analysis
Methods: statistical
Line: profiles
ISM: clouds
Radiative transfer
Författare
Antoine Roueff
Université de Toulon
J. Pety
Observatoire de Paris
Institut de Radioastronomie Millimétrique (IRAM)
M. Gerin
Observatoire de Paris
L. Segal
Université de Toulon
Institut de Radioastronomie Millimétrique (IRAM)
J.R. Goicoechea
Consejo Superior de Investigaciones Científicas (CSIC)
Harvey Liszt
National Radio Astronomy Observatory
P. Gratier
Laboratoire d'Astrophysique de Bordeaux
Ivana Bešlić
Observatoire de Paris
Lucas Einig
Institut de Radioastronomie Millimétrique (IRAM)
Université Grenoble Alpes
Mathilde Gaudel
Observatoire de Paris
Jan Orkisz
Chalmers, Rymd-, geo- och miljövetenskap, Astronomi och plasmafysik
Pierre Palud
Observatoire de Paris
Université de Lille
Miriam G. Santa-Maria
Consejo Superior de Investigaciones Científicas (CSIC)
Victor De Souza Magalhaes
Institut de Radioastronomie Millimétrique (IRAM)
Antoine Zakardjian
Institut de Recherche en Astrophysique et Planétologie (IRAP)
Sébastien Bardeau
Institut de Radioastronomie Millimétrique (IRAM)
E. Bron
Observatoire de Paris
Pierre Chainais
Université de Lille
Simon Coudé
Environment Environment
Harvard-Smithsonian Center for Astrophysics
K. Demyk
Institut de Recherche en Astrophysique et Planétologie (IRAP)
Viviana Guzman
Pontificia Universidad Catolica de Chile
A. Hughes
Institut de Recherche en Astrophysique et Planétologie (IRAP)
David Languignon
Observatoire de Paris
F. Levrier
Laboratoire de Physique de l’Ecole Normale Supérieure
D. C. Lis
California Institute of Technology (Caltech)
Jacques Le Bourlot
Observatoire de Paris
Franck Le Petit
Observatoire de Paris
Nicolas Peretto
Cardiff University
Evelyne Roueff
Observatoire de Paris
A. Sievers
Institut de Radioastronomie Millimétrique (IRAM)
Pierre Antoine Thouvenin
Université de Lille
Astronomy and Astrophysics
0004-6361 (ISSN) 1432-0746 (eISSN)
Vol. 686 A255Ämneskategorier (SSIF 2011)
Astronomi, astrofysik och kosmologi
Atom- och molekylfysik och optik
Sannolikhetsteori och statistik
DOI
10.1051/0004-6361/202449148